Strong periodic driving can be used to control the properties of interacting quantum systems. For example, in solid state experiments, ultrashort laser pulses are employed to tune the charge order as well as magnetic and superconducting properties of materials. This method, known as Floquet engineering, can also be used in cold atoms experiments to realize new models. In this seminar, I will present two experimental examples .of novel effective Hamiltonians. First, I will report on the realisation of the Haldane model and the characterisation of its topological band-structure, using non-interacting ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry, which is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, induced through circular modulation of the lattice position. This opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berry-curvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. Second, I will discuss the influence of interparticle interactions in periodically driven optical lattices. In the high-frequency regime, the effective description of the many-body system by a renormalized tunnelling amplitude remains valid, as demonstrated by comparing our results to an equivalent static system. Furthermore, when driving at a frequency close to the interaction energy, anti-ferromagnetic correlations can be enhanced or even switched to ferromagnetic ordering.